Finite Group Databasebeta

← #29663245

Subgroups — #29663245

Order 15616.

594 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456969C211yesmaximal, characteristic
2#21456766C211yesmaximal, characteristic
3#498×D61C211yesmaximal, characteristic
4#21454748C211yesmaximal, characteristic
5#21445328C211yesmaximal, characteristic, complemented
6#21445327C211yesmaximal, characteristic, complemented
7#21445324C211yesmaximal, characteristic, complemented
8#21445323C211yesmaximal, characteristic, complemented
9#21445202C211yesmaximal, characteristic, complemented
10#21445201C211yesmaximal, characteristic, complemented
11#21445198C211yesmaximal, characteristic, complemented
12#21444564C211yesmaximal, characteristic
13#21444502C211yesmaximal, characteristic
14#21444498C211yesmaximal, characteristic
15C61×#1672C211yesmaximal, characteristic, complemented
16#16840316C2211yescharacteristic
17C4⋊Q8×D61C2211yescharacteristic
18C4⋊Q8×D61C2211yescharacteristic
19#16840166—21no—
20#16840160C2211yescharacteristic
21#16840159—21no—
22#16840159—21no—
23#16840158C2211yescharacteristic
24#16840158C2211yescharacteristic
25#16840140—21no—
26#16840111—21no—
27#16840111—21no—
28#16840099—21no—
29#16840096—21no—
30#16840058C2211yescharacteristic
31#16840057C2211yescharacteristic
32#16840054C2211yescharacteristic
33#16839973C2211yescharacteristic
34#16839972C2211yescharacteristic
35#16839969C2211yescharacteristic
36#16839919—21no—
37#16839916—21no—
38#16839893C2211yescharacteristic
39#16839891—21no—
40#16839889C2211yescharacteristic
41C8×Dic122—21no—
42C8×Dic122C2211yescharacteristic
43#16839814C2211yescharacteristic
44#16839814C2211yescharacteristic
45#106×D61—21no—
46#106×D61—21no—
47#16839787—21no—
48#16839784C2211yescharacteristic
49#16839716—21no—
50C4×C8×D61C2211yescharacteristic
51#16839514C2211yescharacteristic
52#16839514C2211yescharacteristic
53#16839513C2211yescharacteristic
54#16839511C2211yescharacteristic
55#16839510C2211yescharacteristic
56#16839510C2211yescharacteristic
57#16839509C2211yescharacteristic
58#16839508C2211yescharacteristic
59#16839507C2211yescharacteristic
60C61×#498C2211yescharacteristic
61C61×#477C2211yescharacteristic
62C61×#462C2211yescharacteristic
63C8×Q8×C61C2211yescharacteristic
64C61×#334C2211yescharacteristic
65C61×#333C2211yescharacteristic
66C61×#332C2211yescharacteristic
67C2×Q8×D61—21no—
68C2×Q8×D61—21no—
69C2×Dic244—21no—
70C2×#11758202—21no—
71C2×#11758202—21no—
72C2×#11758189—21no—
73C2×C8×D61D411yescharacteristic
74C2×C8×D61D411yescharacteristic
75#14519777C2311yescharacteristic
76#14519777C2311yescharacteristic
77#14519776—21no—
78#14519776—21no—
79#14519776—21no—
80#14519776—21no—
81#14519776D411yescharacteristic
82#14519775—21no—
83#14519775—21no—
84#14519775D411yescharacteristic
85#14519767—21no—
86#14519757D411yescharacteristic
87#14519755—21no—
88#14519753D411yescharacteristic
89C4×Dic122—21no—
90C4×Dic122C2311yescharacteristic
91#14519734—21no—
92C4⋊C4×D61—21no—
93C4⋊C4×D61—21no—
94C4⋊C4×D61—21no—
95C4⋊C4×D61—21no—
96C42×D61C2311yescharacteristic
97#14519711—21no—
98#14519710—21no—
99#14519710—21no—
100#14519709—21no—
101#14519709—21no—
102#14519708—21no—
103#14519708—21no—
104#14519708—21no—
105#14519708—21no—
106C4⋊#92418—21no—
107C4⋊#92418C2311yescharacteristic
108C4⋊#92418C2311yescharacteristic
109C4⋊#92418C2311yescharacteristic
110#14519706—21no—
111#14519706—21no—
112#14519706—21no—
113#14519702—21no—
114#14519702—21no—
115#14519701—21no—
116#14519701—21no—
117#14519700—21no—
118#14519700—21no—
119#14519689—21no—
120#14519689—21no—
121#14519688—21no—
122#14519687—21no—
123C4×#92418C2311yescharacteristic
124C8×Dic61—21no—
125C8×Dic61—21no—
126C8×Dic61—21no—
127C8×Dic61D411yescharacteristic
128C8×Dic61D411yescharacteristic
129C2×Q16×C61—21no—
130C4⋊Q8×C61C2311yescharacteristic
131C4⋊Q8×C61C2311yescharacteristic
132C4×Q8×C61C2311yescharacteristic
133#107×C61—21no—
134#106×C61—21no—
135#106×C61—21no—
136C4⋊C8×C61—21no—
137C4⋊C8×C61C2311yescharacteristic
138C4⋊C8×C61C2311yescharacteristic
139C4⋊C8×C61C2311yescharacteristic
140#103×C61—21no—
141#103×C61—21no—
142C4×C8×C61—21no—
143C4×C8×C61C2311yescharacteristic
144C2×Q8×C61—21no—
145C2×Q8×C61—21no—
146C2×Q8×C61C2×D411yescharacteristic
147Q8×D61—81no—
148Q8×D61—81no—
149Q8×D61—82no—
150C2×C4×D61—41no—
151C2×C4×D61—41no—
152C2×C4×D61C2×D411yescharacteristic
153C2×C4×D61C2×D411yescharacteristic
154C2×C4×D61#4111yescharacteristic
155C2×Dic122—21no—
156C2×Dic122—21no—
157C2×Dic122—21no—
158C2×Dic122—41no—
159C2×Dic122—41no—
160C2×Dic122C2×D411yescharacteristic
161Q16×C61—81no—
162C2×C8×C61—21no—
163C2×C8×C61—21no—
164C2×C8×C61—21no—
165C2×C8×C61C2×D411yescharacteristic
166C2×C8×C61C2×D411yescharacteristic
167C4⋊C4×C61—21no—
168C4⋊C4×C61—21no—
169C4⋊C4×C61—21no—
170C4⋊C4×C61—21no—
171C4⋊C4×C61—21no—
172C4⋊C4×C61C2×D411yescharacteristic
173C42×C61—21no—
174C42×C61C2411yescharacteristic
175#11758202—81no—
176#11758202—81no—
177#11758198—21no—
178#11758198—21no—
179C4⋊Dic61—21no—
180C4⋊Dic61—21no—
181C4⋊Dic61—21no—
182C4⋊Dic61—21no—
183C4⋊Dic61—21no—
184C4⋊Dic61C2×D411yescharacteristic
185#11758196—21no—
186#11758196—21no—
187#11758196—21no—
188#11758196—21no—
189#11758196—21no—
190#11758196—41no—
191#11758196—41no—
192#11758196—41no—
193#11758196—41no—
194C4×Dic61—21no—
195C4×Dic61C2×D411yescharacteristic
196C4×Dic61C2×D411yescharacteristic
197C4×Dic61#4111yescharacteristic
198C2×#92418—21no—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418C2×D411yescharacteristic
202C2×#92418C2×D411yescharacteristic
203Dic244—81no—
204#11758189—42no—
205C8×D61—22no—
206C8×D61Q1614yescomplemented
207C22×D61#12111yescharacteristic
208Q8×C61—21no—
209Q8×C61—21no—
210Q8×C61—41no—
211Q8×C61—41no—
212Q8×C61—81no—
213C2×C4×C61—21no—
214C2×C4×C61—21no—
215C2×C4×C61—41no—
216C2×C4×C61—41no—
217C2×C4×C61C22×D411yescharacteristic
218C2×C4×C61C22×D411yescharacteristic
219C2×C4×C61C2×#4111yescharacteristic
220C2×Dic61—21no—
221C2×Dic61—21no—
222C2×Dic61—41no—
223C2×Dic61—41no—
224C2×Dic61#12111yescharacteristic
225C2×Dic61#12111yescharacteristic
226C2×Dic61#12111yescharacteristic
227C4×D61—21no—
228C4×D61—21no—
229C4×D61—22no—
230C4×D61—82no—
231C4×D61—82no—
232C4×D61C2×Q1612yes—
233C4×D61#13712yes—
234Dic122—21no—
235Dic122—21no—
236Dic122—42no—
237Dic122—41no—
238Dic122—41no—
239Dic122—82no—
240Dic122—82no—
241Dic122—81no—
242C8×C61—21no—
243C8×C61—41no—
244C8×C61—41no—
245C8×C61—41no—
246C8×C61C2×Q1612yes—
247#92418—21no—
248#92418—41no—
249#92418—41no—
250#92418—41no—
251#92418C2×Q1612yes—
252#19207—611nomaximal, Sylow
253C22×C61C2×#12111yescharacteristic
254C2×D61—21no—
255C2×D61—21no—
256C2×D61#46212yes—
257C4×C61—21no—
258C4×C61—41no—
259C4×C61—41no—
260C4×C61—81no—
261C4×C61—81no—
262C4×C61C22×Q1611yescharacteristic
263C4×C61C2×#13711yescharacteristic
264C4×C61#57711yescharacteristic
265C4×C61#57711yescharacteristic
266Dic61—21no—
267Dic61—41no—
268Dic61—41no—
269Dic61—81no—
270Dic61—81no—
271Dic61#46212yes—
272Dic61#47112yes—
273#3230—611no—
274#3209—611no—
275C2×#498—611no—
276#2960—611no—
277#1692—611no—
278#1692—611no—
279#1692—611no—
280#1692—611no—
281#1672—611no—
282#1672—611no—
283#1672—611no—
284#1672D6111yescharacteristic, complemented
285#1564—611no—
286#1549—611no—
287#1548—611no—
288C2×C61C2×#46211yescharacteristic
289C2×C61#305711yescharacteristic
290C2×C61C2×#47111yescharacteristic
291D61—22no—
292#533—611no—
293C2×C4⋊Q8—611no—
294C2×C4⋊Q8—611no—
295#500—1221no—
296#498—611no—
297#498—611no—
298#498—611no—
299#498—1221no—
300#498—1221no—
301#498C2×D6111yescharacteristic
302#494—1221no—
303#487—1221no—
304#487—1221no—
305#484—1221no—
306#484—1221no—
307#477—611no—
308#477—611no—
309#477—611no—
310#477C2×D6111yescharacteristic
311#462—611no—
312#462—611no—
313#462—611no—
314#462C2×D6111yescharacteristic
315#451—1221no—
316#451—1221no—
317#446—611no—
318#446—611no—
319#446—1221no—
320C8×Q8—611no—
321C8×Q8—1221no—
322C8×Q8C2×D6111yescharacteristic
323#431—611no—
324#431—611no—
325C2×#106—1221no—
326C2×#106—1221no—
327#424—1221no—
328#423—611no—
329#405—1221no—
330C2×C4×C8—611no—
331#335—611no—
332#335—611no—
333#334—611no—
334#334C2×D6111yescharacteristic
335#333—611no—
336#333—611no—
337#333—611no—
338#333C2×D6111yescharacteristic
339#332—611no—
340#332—611no—
341#332—611no—
342#332C2×D6111yescharacteristic
343C61#1920711yescharacteristic, complemented, Sylow
344C22×Q8—1221no—
345C22×Q8—1221no—
346C2×Q16—21no—
347C2×Q16—1221no—
348C2×Q16—1221no—
349C2×Q16—1221no—
350C2×M16—1221no—
351C22×C8—611no—
352C22×C8—611no—
353C4⋊Q8—611no—
354C4⋊Q8—611no—
355C4⋊Q8—611no—
356C4⋊Q8—611no—
357C4⋊Q8—1221no—
358C4⋊Q8—1221no—
359C4⋊Q8—1221no—
360C4⋊Q8—1221no—
361C4⋊Q8—1221no—
362C4⋊Q8—1221no—
363C4⋊Q8C22×D6111yescharacteristic
364C4⋊Q8C22×D6111yescharacteristic
365#125—1221no—
366C22⋊Q8—611no—
367C22⋊Q8—611no—
368C22⋊Q8—1221no—
369C4×Q8—611no—
370C4×Q8—1221no—
371C4×Q8C22×D6111yescharacteristic
372#117—1221no—
373C2×C4⋊C4—1221no—
374C2×C4⋊C4—1221no—
375C2×C4⋊C4—1221no—
376C2×C4⋊C4—1221no—
377C2×C42—611no—
378#107—21no—
379#107—1221no—
380#107—1221no—
381#107—1221no—
382#106—21no—
383#106—21no—
384#106—1221no—
385#106—1221no—
386#106—1221no—
387#106—1221no—
388#106—1221no—
389#106—1221no—
390C4⋊C8—21no—
391C4⋊C8—611no—
392C4⋊C8—611no—
393C4⋊C8—611no—
394C4⋊C8—1221no—
395C4⋊C8—1221no—
396C4⋊C8—1221no—
397C4⋊C8—1221no—
398C4⋊C8C22×D6111yescharacteristic
399C4⋊C8C22×D6111yescharacteristic
400C4⋊C8C22×D6111yescharacteristic
401#103—21no—
402#103—21no—
403#103—1221no—
404#103—1221no—
405#103—1221no—
406#103—1221no—
407#103—1221no—
408#103—1221no—
409C22⋊C8—1221no—
410C22⋊C8—1221no—
411#97—1221no—
412#97—1221no—
413C4×C8—21no—
414C4×C8—611no—
415C4×C8—611no—
416C4×C8—611no—
417C4×C8—1221no—
418C4×C8—1221no—
419C4×C8—1221no—
420C4×C8C22×D6111yescharacteristic
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—611no—
424C2×Q8—1221no—
425C2×Q8—1221no—
426C2×Q8—1221no—
427C2×Q8—4881no—
428C2×Q8—4881no—
429C2×Q8—4882no—
430C2×Q8—2441no—
431C2×Q8—2441no—
432C2×Q8D4×D6111yescharacteristic
433C22×C4—611no—
434C22×C4—611no—
435C22×C4—611no—
436C22×C4—2441no—
437C22×C4—2441no—
438Q16—81no—
439Q16—4881no—
440Q16—4881no—
441Q16—4881no—
442M16—2442no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—611no—
447C2×C8—614no—
448C2×C8—611no—
449C2×C8—1222no—
450C2×C8—1221no—
451C2×C8—1221no—
452C2×C8—1221no—
453C2×C8D4×D6111yescharacteristic
454C2×C8D4×D6111yescharacteristic
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—611no—
461C4⋊C4—1221no—
462C4⋊C4—1221no—
463C4⋊C4—1221no—
464C4⋊C4—1221no—
465C4⋊C4—1221no—
466C4⋊C4—1221no—
467C4⋊C4—1221no—
468C4⋊C4—1221no—
469C4⋊C4—1221no—
470C4⋊C4—1221no—
471C4⋊C4—2441no—
472C4⋊C4—2441no—
473C4⋊C4—2441no—
474C4⋊C4—2441no—
475C4⋊C4D4×D6111yescharacteristic
476C22⋊C4—1221no—
477C22⋊C4—1221no—
478C42—21no—
479C42—611no—
480C42—611no—
481C42—611no—
482C42—1221no—
483C42C23×D6111yescharacteristic
484C23—611no—
485Q8—21no—
486Q8—21no—
487Q8—41no—
488Q8—41no—
489Q8—81no—
490Q8—1221no—
491Q8—1221no—
492Q8—4881no—
493Q8—4882no—
494Q8—4882no—
495Q8—2442no—
496Q8—2441no—
497Q8—2441no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—611no—
503C2×C4—611no—
504C2×C4—612no—
505C2×C4—612no—
506C2×C4—611no—
507C2×C4—1222no—
508C2×C4—1221no—
509C2×C4—1221no—
510C2×C4—1221no—
511C2×C4—1221no—
512C2×C4—4882no—
513C2×C4—4882no—
514C2×C4—2441no—
515C2×C4—2441no—
516C2×C4C2×D4×D6111yescharacteristic
517C2×C4C2×D4×D6111yescharacteristic
518C2×C4#41×D6111yescharacteristic
519C8—21no—
520C8—41no—
521C8—41no—
522C8—41no—
523C8—612no—
524C8—1221no—
525C8—2441no—
526C8—2441no—
527C8—2441no—
528C8Q16×D6112yes—
529C22—612no—
530C22—1221no—
531C22—1221no—
532C22#121×D6111yescharacteristic
533C4—21no—
534C4—41no—
535C4—41no—
536C4—81no—
537C4—81no—
538C4—612no—
539C4—612no—
540C4—1221no—
541C4—4881no—
542C4—4881no—
543C4—2441no—
544C4—2441no—
545C4C2×Q16×D6111yescharacteristic
546C4#137×D6111yescharacteristic
547C4#1684056811yescharacteristic
548C4#1684056911yescharacteristic
549C2—1222no—
550C2#462×D6111yescharacteristic
551C2#2145545311yescharacteristic
552C2#471×D6111yescharacteristic
subgroupG/H
centerC22#121×D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#1672C2
socleC22×C61C2×#121
prime radicalC22×D61#121
hypercenter#1672D61
hypocenterC61#19207
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #1672

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
5. #21445328C2semidirect
6. #21445327C2semidirect
7. #21445324C2semidirect
8. #21445323C2semidirect
9. #21445202C2semidirect
10. #21445201C2semidirect
11. #21445198C2semidirect
15. C61×#1672C2semidirect
206. C8×D61Q16semidirect
284. #1672D61semidirect
343. C61#19207semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#214569692
#214567662
#498×D612
#214547482
#214453282
#214453272
#214453242
#214453232
#214452022
#214452012
#214451982
#214445642
#214445022
#214444982
C61×#16722
#1920761